Simplify the following expression: $ t = \dfrac{-3z - 9}{6z - 1} + \dfrac{-7}{4} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-3z - 9}{6z - 1} \times \dfrac{4}{4} = \dfrac{-12z - 36}{24z - 4} $ Multiply the second expression by $\dfrac{6z - 1}{6z - 1}$ $ \dfrac{-7}{4} \times \dfrac{6z - 1}{6z - 1} = \dfrac{-42z + 7}{24z - 4} $ Therefore $ t = \dfrac{-12z - 36}{24z - 4} + \dfrac{-42z + 7}{24z - 4} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-12z - 36 - 42z + 7}{24z - 4} $ $t = \dfrac{-54z - 29}{24z - 4}$